# Peter L. Antonelli (Mathematician)

Peter Louis Antonelli | |
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Born | Syracuse, New York | March 5, 1941

Died | February 14, 2020 | (aged 78)

Nationality | American |

Citizenship | United States of America |

Alma mater | Syracuse University |

Occupation | Mathematician |

**Peter Louis Antonelli** (March 5, 1941 - Feb. 14, 2020) was an American mathematician who worked on mathematical biology/Theoretical ecology|ecology^{[1]}^{[2]}^{[3]}^{[4]}, evolution^{[5]}^{[6]}^{[7]}^{[8]}^{[9]}, Finsler geometry^{[10]}^{[11]}^{[12]}, algebraic and differential topology^{[13]}^{[14]}, seismology^{[15]}, and a number of other topics^{[16]}^{[17]}^{[18]}^{[19]}. He is most well-known for his mathematical models of coral bleaching^{[20]}^{[21]} and crown-of-thorns starfish predation on the Great Barrier Reef^{[22]}^{[23]}^{[24]}.

## Overview

Born in Syracuse, New York, he attended Syracuse University for both his undergraduate and graduate studies (Ph.D., 1967)^{[25]}, followed by a short period as assistant professor at the University of Tennessee, Knoxville (1967-1968), an NSF post-doctoral fellowship at the Institute for Advanced Study, Princeton University (1968-1970), and finally a professor position at the University of Alberta, Canada, where he stayed for the remainder of his career.^{[26]}^{[27]} During his time as a professor, he advised a plethora of graduate students and over 37 post-doctoral students, including Vlastimil Krivan, Brad Lackey, Thomas Zastawniak, Ioan Bucataru, Dragos Hrimiuc and many others^{[26]}. In 2006, he moved to Brazil with his wife and colleague S.F. Rutz, where he was a visiting professor at Federal University of Pernambuco, Recife^{[28]}. In February 2020, he passed away in Recife|Recife, Brazil, at the age of 78.

## Contributions to mathematics

Peter L. Antonelli's Ph.D. thesis was entitled "Structure Theory for Montgomery-Samelson Fiberings Between Manifolds" (advisor: Prof. Erik Hemmingsen)^{[29]}. His results were published in some important Journals, including Proceedings of the American Mathematical Society^{[30]} and Bulletin of the American Mathematical Society^{[31]}Bulletin of the American Mathematical Society|. He put forward a structure theory of Montgomery-Samelson fiberings and studied these fiberings in spheres, along with those having finite singular sets. He worked with Peter J. Kahn (student of renowned mathematician John Milnor) and Dan Burghelea to solve some difficult problems on the diffeomorphism group of manifolds including spheres and exotic spheres^{[32]}^{[33]}^{[14]}. After 1970, his interests shifted towards applied mathematics, especially applications of differential geometry to developmental biology, ecology, and genetics^{[26]}. As a visiting professor in the biology department at the University of Sussex (1972-1973), he learned about these branches of applied mathematics, pursuing interests that had been sparked during a short stint as a United States Public Health Service Fellow in mathematical biology at the University of Chicago (1963-1964)^{[26]}.

### An early start, and a rich career

In 1955, on his 14^{th} birthday, Peter L. Antonelli was given a calculus text book that sparked his passion for mathematics^{[26]}. Three years later, he won a mathematics contest and acquired a copy of Luther P. Eisenhart's *Riemannian Geometry*, which he kept for the rest of his life^{[26]}. In these early years, his interests were focused on physics, especially general relativity, and he became a precocious figure at seminars in the department of physics at Syracuse University^{[26]}. As a young adult, he focused on strange mathematical objects such as special groups of diffeomorphisms and exotic spheres^{[26]}. Later on, he became a proponent of using mathematics as a tool for solving problems across the natural Sciences. Over a period of 50 years, he found common languages with specialists in a variety of fields including Roger Bradbury, Paul Sammarco, Nicholas D. Kazarinoff, Curtis Strobeck, Robert Elliot, K. Morgan, and Roger Seymour, to name just a few. Collaborating with these specialists and with his post-doctoral students, he constructed powerful mathematical models that yielded practical results in several fields of both pure and applied mathematics^{[26]}.

During the course of his career, Peter L. Antonelli published well over 120 research papers in a variety of domains including non-linear mechanics, Hamiltonian systems, diffusion theory, stochastic calculus and stochastic geometry, geometric probability, differential game theory, bifurcation theory, geometry of paths, and Riemannian, Finslerian and Lagrangian geometries^{[26]}. He made especially notable contributions to the fields of Finslerian and Lagrangian geometry, beginning with the introduction of a mathematical model for treating Volterra-Hamilton equations in biology^{[34]}. He clarified the concept of constant Finslerian connection (with Makoto Matsumoto), explored the stability of geodesics for special m^{th}-root metrics (with Hideo Shimada), discovered and studied a new class of Lagrangian manifold (with Mihai Anastasiei and Dragos Hrimiuc), and developed a stochastic calculus and diffusion theory on Finsler manifolds (with Thomas Zastawniak), which has become the standard text in the field^{[35]}^{[26]}. He also published a fundamental book on applications of Finsler geometry to Physics and Biology (with Makoto Matsumoto and Roman Ingarden)^{[36]}. Peter L. Antonelli left a long-lasting mark on the geometry of non-Riemannian metrics, which now bear his name ("Antonelli Spaces")^{[26]}.

In 1987 he was awarded a McCalla Professorship (University of Alberta) for research excellence. In 2001, Peter L. Antonelli was awarded the degree of Honorary Professor from the oldest university in Romania (Alexandru loan Cuza University, Iași, Romania)^{[26]}. He was known as an eccentric and enthusiastic teacher and took great joy in introducing students to mathematical research opportunities^{[26]}. He was an editor for a number of scientific journals and volumes and published over a dozen books, mostly targeting stochastic and deterministic processes on Finsler and Riemannian manifolds^{[26]}^{[37]}. He liked to travel the world giving lectures, attending scientific meetings, and organizing sessions at international conferences^{[26]}. In his final years, he was an active member of the Researchgate community, publishing many preprints and interacting with new and old colleagues from around the world^{[38]}.

## References

- ↑ Antonelli, P. L.; Cantalice, J. R. B.; Rutz, S. F.; Filho, J. A. Silva; Nunes, E. O. S. (2018-11-26). "Exchange of plant growth energy and hydrodynamical energy in a Riverine ecosystem".
*Nonlinear Studies*.**25**(4): 807–826. - ↑ Antonelli, P. L.; Zastawniak, T. J. (1998), Antonelli, Peter L.; Lackey, Bradley C. (eds.), "Density Dependent Host/Parasite Systems of Rothschild Type and Finslerian Diffusion",
*The Theory of Finslerian Laplacians and Applications*, Mathematics and Its Applications, Dordrecht: Springer Netherlands, pp. 13–31, doi:10.1007/978-94-011-5282-2_2, ISBN 978-94-011-5282-2, retrieved 2022-01-14 - ↑ Antonelli, Peter Louis; Rutz, Solange da Fonseca; Strychar, Kevin B. (2021-02-22). "Heat stress on Scleractinian corals: Its symbionts in evolution".
*Nonlinear Studies*.**28**(1): 189–196. - ↑ Antonelli, P. L.; Leandro, C. G.; Rutz, S. F. (2016). "PHENOTYPIC DEFORMATION: THE ROLE OF ALLOMETRY AND THE GOLDEN RATIO".
*International Journal of Applied Mathematics*.**29**(4): 485–503. doi:10.12732/ijam.v29i4.6. - ↑ Antonelli, P. L.; Rutz, S. F.; Jr, G. S. Ferreira (2019-08-28). "Remarks on modelling serial endosymbiosis and evolution of eukaryote tissue formation".
*Nonlinear Studies*.**26**(3): 653–662. - ↑ Antonelli, P.; Bradbury, R.; Křivan, V.; Shimada, H. (1993-12-01). "A dynamical theory of heterochrony: time-sequencing changes in ecology, development and evolution".
*Journal of Biological Systems*.**01**(4): 451–487. doi:10.1142/S0218339093000264. - ↑ Antonelli, P. L.; Leandro, C. G.; Rutz, S. F. (2016-11-26). "STOCHASTIC CANALIZATION OF PHENOTYPIC DEFORMATIONS DURING ONTOGENESIS".
*International Journal of Applied Mathematics*.**29**(6): 655–671. doi:10.12732/ijam.v29i6.2. - ↑ Antonelli, Peter L.; Rutz, Solange F.; Hirakawa, Carlos E. (2011-12-01). "The mathematical theory of endosymbiosis I".
*Nonlinear Analysis: Real World Applications*.**12**(6): 3238–3251. doi:10.1016/j.nonrwa.2011.05.023. - ↑ "Researchers Show Evolutionary Theory Adds Up".
*ScienceDaily*. Retrieved 2022-01-14. - ↑ Antonelli, Peter L.; Lackey, Bradley C., eds. (1998).
*The Theory of Finslerian Laplacians and Applications*. doi:10.1007/978-94-011-5282-2. ISBN 978-94-010-6223-7. - ↑
*Handbook of Finsler Geometry*. - ↑ Antonelli, P. L.; Hrimiuc, D. (1996), Antonelli, P. L.; Miron, R. (eds.), "A New Class Of Spray-Generating Lagrangians",
*Lagrange and Finsler Geometry: Applications to Physics and Biology*, Fundamental Theories of Physics, Dordrecht: Springer Netherlands, pp. 81–92, doi:10.1007/978-94-015-8650-4_7, ISBN 978-94-015-8650-4, retrieved 2022-01-14 - ↑ Antonelli, P. L. (August 1971). "On Stable Diffeomorphism of Exotic Spheres in the Metastable Range".
*Canadian Journal of Mathematics*.**23**(4): 579–587. doi:10.4153/CJM-1971-065-x. - ↑
^{14.0}^{14.1}Antonelli, P.; Burghelea, D.; Kahn, P. J. (July 1970). "Gromoll groups, ${\text{Diff}}\,S^n$ and bilinear constructions of exotic spheres".*Bulletin of the American Mathematical Society*.**76**(4): 772–777. doi:10.1090/S0002-9904-1970-12544-74. - ↑ Antonelli, P. L.; Rutz, S. F.; Slawinski, M. A. (2003), Anastasiei, M.; Antonelli, P. L. (eds.), "A Geometrical Foundation for Seismic Ray Theory Based on Modern Finsler Geometry",
*Finsler and Lagrange Geometries: Proceedings of a Conference held on August 26–31, Iaşi, Romania*, Dordrecht: Springer Netherlands, pp. 17–54, doi:10.1007/978-94-017-0405-2_3, ISBN 978-94-017-0405-2, retrieved 2022-01-14 - ↑ Antonelli, P.; Rutz, S.; Rego, Moraes (2015). "Analytical Non-linear Modular Dynamics for Balanced Exploitation of Fisheries".
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(help) - ↑ Antonelli, P. L.; Rutz, S. F.; Cantalice, J. R. B. (2016-02-27). "Carbon cycles in tree stands from KCC theory: Discounted production due to litter decomposition".
*Nonlinear Studies*.**23**(1): 111–115. - ↑ Antonelli, P. L.; Rutz, S. F.; Junior, R. V. S. (2013-11-13). "Environmental Analysis of Impact of Transgenic Crops".
*International Journal of Applied Mathematics*.**26**(4): 515–524. doi:10.12732/ijam.v26i4.10. - ↑ Antonelli, Peter L. (1992-03-01). "The Algorithmic Beauty of Plants (Przemyslaw Prusinkiewicz and Aristid Lindenmayer)".
*SIAM Review*.**34**(1): 142–143. doi:10.1137/1034030. - ↑ Antonelli, Peter L.; Rutz, Solange F.; Sammarco, Paul W.; Strychar, Kevin B. (2016-12-01). "Evolution of symbiosis in hermatypic corals: A model of the past, present, and future".
*Nonlinear Analysis: Real World Applications*.**32**: 389–402. doi:10.1016/j.nonrwa.2016.05.004. - ↑ "A coral bleaching model | Antonelli, Peter L.; Rutz, Solange F.; Sammarco, Paul W.; Strychar, Kevin B. | download".
*zh.booksc.eu*. Retrieved 2022-01-14. - ↑ Antonelli, Peter; Auger, Pierre (1995). "Corals and Starfish Devastation of the Great Barrier Reef: Aggregation Methods".
*Acta Biotheoretica*.**43**(4): 481–493. doi:10.1007/BF00713566. - ↑ Antonelli, P.; Auger, P.; Bradbury, R. (1998-02-01). "Corals and starfish waves on the great barrier reef: Analytical trophodynamics and 2-patch aggregation methods".
*Mathematical and Computer Modelling*.**27**(4): 121–135. doi:10.1016/S0895-7177(98)00012-0. - ↑ "Nonlinear prediction of crown–of–thorns outbreaks on the great barrier reef | Antonelli, P.; Bradbury, R.; Buck, R.; Reichelt, R.; Elliott, R. | download".
*ur.booksc.me*. Retrieved 2022-01-14. - ↑ "Alumni".
*College of Arts & Sciences at Syracuse University*. Retrieved 2022-01-16. - ↑
^{26.00}^{26.01}^{26.02}^{26.03}^{26.04}^{26.05}^{26.06}^{26.07}^{26.08}^{26.09}^{26.10}^{26.11}^{26.12}^{26.13}^{26.14}^{26.15}Anastasiei, Mihai; Antonelli, P. L. (2013-06-29).*Finsler and Lagrange Geometries: Proceedings of a Conference held on August 26–31, Iaşi, Romania*. Springer Science & Business Media. ISBN 978-94-017-0405-2. - ↑ "Retired Faculty | Mathematical and Statistical Sciences".
*www.ualberta.ca*. Retrieved 2022-01-14. - ↑ "Peter Louis Antonelli".
*Escavador*(in português do Brasil). Retrieved 2022-01-16. - ↑ "Alumni".
*College of Arts & Sciences at Syracuse University*. Retrieved 2022-01-16. - ↑ Antonelli, P. L. (1969). "Montgomery-Samelson singular fiberings of spheres".
*Proceedings of the American Mathematical Society*.**22**(1): 247–250. doi:10.1090/S0002-9939-1969-0253353-4. - ↑ Antonelli, P.; Burghelea, D.; Kahn, P. J. (July 1970). "Gromoll groups, ${\text{Diff}}\,S^n$ and bilinear constructions of exotic spheres".
*Bulletin of the American Mathematical Society*.**76**(4): 772–777. doi:10.1090/S0002-9904-1970-12544-7. - ↑ Antonelli, P.; Burghelea, D.; Kahn, P. J. (1972). "The non-finite homotopy type of some diffeomorphism groups".
*Topology*.**11**: 1–49. doi:10.1016/0040-9383(72)90021-3. - ↑ Antonelli, Peter L.; Burghelea, Dan; Kahn, Peter J. (1971). "The Concordance-Homotopy Groups of Geometric Automorphism Groups".
*Lecture Notes in Mathematics*.**215**. doi:10.1007/bfb0061176. ISBN 978-3-540-05560-0. - ↑ Antonelli, P. L. (1990-01-01). "A brief introduction to Volterra-Hamilton theory in ecological modelling".
*Mathematical and Computer Modelling*.**13**(6): 19–23. doi:10.1016/0895-7177(90)90004-7. - ↑ Antonelli, P. L.; Zastawniak, T. J. (1998), Antonelli, Peter L.; Lackey, Bradley C. (eds.), "Stochastic Calculus on Finsler Manifolds and an Application in Biology",
*The Theory of Finslerian Laplacians and Applications*, Mathematics and Its Applications, Dordrecht: Springer Netherlands, pp. 63–88, doi:10.1007/978-94-011-5282-2_5, ISBN 978-94-011-5282-2, retrieved 2022-01-16 - ↑ Antonelli, P. L.; Ingarden, R. S.; Matsumoto, M. (1993).
*The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology*. doi:10.1007/978-94-015-8194-3. ISBN 978-90-481-4341-2. - ↑ "Peter Louis Antonelli".
*Escavador*(in português do Brasil). Retrieved 2022-01-16. - ↑ "Peter L. Antonelli (Researchgate)".
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